Computational Shape Understanding for 3D Reconstruction and Modeling
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The physical and the digital world are becoming tightly connected as we see an increase in thevariety of 2D and 3D acquisition devices, e.g., smartphones, digital camera, scanners, commercialdepth sensors. The recent advances in the acquisition technologies facilitate the data captureprocess and make it accessible for casual users. This tremendous increase in the digital contentcomes with many application opportunities including medical applications, industrial simulations,documentation of cultural artifacts, visual effects etc.The success of these digital applications depends on two fundamental tasks. On the one hand,our goal is to obtain an accurate and high-quality digital representation of the physical world. Onthe other hand, performing high-level shape analysis, e.g. structure discovery in the underlyingcontent, is crucial. Both of these tasks are extremely challenging due to the large amount ofavailable digital content and the varying data quality of this content including noisy and partialdata measurements. Nonetheless, there exists a tight coupling between these two tasks: accuratelow-level data measurement makes it easier to perform shape analysis, whereas use of suitablesemantic priors provides opportunities to increase the accuracy of the digital data.In this dissertation, we investigate the benefits of tackling the low-level data measurementand high-level shape analysis tasks in a coupled manner for 3D reconstruction and modelingpurposes. We specifically focus on image-based reconstruction of urban areas where we exploitthe abundance of symmetry as the principal shape analysis tool. Use of symmetry and repetitionsare reinforced in architecture due to economic, functional, and aesthetic considerations. Weutilize these priors to simultaneously provide non-local coupling between geometric computationsand extract semantic information in urban data sets.Concurrent to the advances in 3D geometry acquisition and analysis, we are experiencing arevolution in digital manufacturing. With the advent of accessible 3D fabrication methods suchas 3D printing and laser cutting, we see a cyclic pipeline linking the physical and the digitalworlds. While we strive to create accurate digital replicas of real-world objects on one hand,there is a growing user-base in demand of manufacturing the existing content on the other hand.Thus, in the last part of this dissertation, we extend our shape understanding tools to the problemof designing and fabricating functional models. Each manufacturing device comes withtechnology-specific limitations and thus imposes various constraints on the digital models thatcan be fabricated. We demonstrate that, a good level of shape understanding is necessary to optimize the digital content for fabrication.